Simplify the following expression: $ q = \dfrac{4}{5} - \dfrac{n + 5}{-n + 9} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-n + 9}{-n + 9}$ $ \dfrac{4}{5} \times \dfrac{-n + 9}{-n + 9} = \dfrac{-4n + 36}{-5n + 45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{n + 5}{-n + 9} \times \dfrac{5}{5} = \dfrac{5n + 25}{-5n + 45} $ Therefore $ q = \dfrac{-4n + 36}{-5n + 45} - \dfrac{5n + 25}{-5n + 45} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-4n + 36 - (5n + 25) }{-5n + 45} $ Distribute the negative sign: $q = \dfrac{-4n + 36 - 5n - 25}{-5n + 45}$ $q = \dfrac{-9n + 11}{-5n + 45}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{9n - 11}{5n - 45}$